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Popular >

derivative of f(x)=(e^x)/(x^2+6)

Solution

derivative of

f (x) = \frac{e ^{x}}{x ^{2} + 6}

Solution

\frac{e ^{x} ( x ^{2} + 6 ) - 2 x e ^{x}}{( x ^{2} + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 6})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{x} ) ( x ^{2} + 6 ) - \frac{d}{d x} ( x ^{2} + 6 ) e ^{x}}{( x ^{2} + 6 ) ^{2}}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x^{2} + 6) = 2 x

= \frac{e ^{x} ( x ^{2} + 6 ) - 2 x e ^{x}}{( x ^{2} + 6 ) ^{2}}

Popular Examples

integral of (3x-1)/((x+4)^2)

\int \frac{3 x - 1}{( x + 4 ) ^{2}} d x

derivative of (sin(t)/(sqrt(1+x^2)))

\frac{d}{d x} (\frac{sin ( t )}{1 + x ^{2}})

integral of x^3e^{ax^4}

\int x^{3} e^{a x^{4}} d x

integral of (2(x^2+1))/(x(x^2+2))

\int \frac{2 ( x ^{2} + 1 )}{x ( x ^{2} + 2 )} d x

limit as x approaches 4-of 1/(x^2-16)

x \to 4 - lim (\frac{1}{x ^{2} - 16})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(e^x)/(x^2+6) ?
The derivative of f(x)=(e^x)/(x^2+6) is (e^x(x^2+6)-2xe^x)/((x^2+6)^2)
What is the first derivative of f(x)=(e^x)/(x^2+6) ?
The first derivative of f(x)=(e^x)/(x^2+6) is (e^x(x^2+6)-2xe^x)/((x^2+6)^2)